Chapter SH, Problem 14.8.10EP

To determine

To factor: the given polynomial

Answer to Problem 14.8.10EP

The required result is $\left(x-2\right)\left(x-6\right)$ .

Explanation of Solution

Given: $x^2-8x+12$

Write the trinomial as the product of two binomials.

Product of first terms is $x^2$ .

  $x^2-8x+12=\left(x+?\right)\left(x+?\right)$

Now find the two terms whose product must be $+12$ .

Try several factors of $+12$ so that sum of the product of outer and inner terms must be $-8x$ .

Try the factors $2,6$ .

  $\begin{array}{l}\left(x+2\right)\left(x+6\right)=x^2+2x+6x+12\\ =x^2+8x+12\end{array}$

It is not true.

Try the factors $-2,-6$ .

  $\begin{array}{l}\left(x-2\right)\left(x-6\right)=x^2-2x-6x+12\\ =x^2-8x+12\end{array}$

It is true.

Hence, the result is $\left(x-2\right)\left(x-6\right)$ .

Conclusion:

Hence, the factorization is $\left(x-2\right)\left(x-6\right)$ .